Conventionally, there has been developed an apparatus for controlling the air-fuel ratio of an internal combustion engine, which apparatus estimates the temperature of a detection element of an air-fuel ratio sensor provided in the exhaust system of the engine, and corrects air-fuel ratio control when the detection element has not yet reached its activation temperature, to thereby reduce fluctuation of the air-fuel ratio (Patent Document 1). Also, there has been developed a technique of estimating the temperature of a gas sensor element provided in the exhaust system of an internal combustion engine through use of a predetermined model, and comparing it with an element temperature calculated from the impedance of the gas sensor element so as to determine the degree of deterioration of the sensor (Patent Document 2).
The above-described estimation of the temperature of the gas sensor element is performed as follows, for example. First, there is prepared a relational expression which represents the relation between the heat reception and radiation amounts of the gas sensor element and exhaust gas temperature, etc. Also, there is prepared a model which represents the relation between the heat reception and radiation amounts and the temperature of the gas sensor element. The heat reception and radiation amounts of the gas sensor element are calculated on the basis of a measurement value provided by a measurement sensor (a temperature sensor or a flow velocity sensor) attached to the exhaust system of the internal combustion engine, and the temperature of the gas sensor element is estimated by the above-described model (an element temperature estimation model).